Question

[Nhân Mã]

Chứng tỏ rằng : \(\dfrac{31}{2}\) . \(\dfrac{32}{2}\) . \(\dfrac{33}{2}\) . .... . \(\dfrac{60}{2}\) = 1 . 3 . 5.... 59

Answer 1

[Lionel Messi]

Ta có:\(\dfrac{31}{2}\).\(\dfrac{32}{2}\).\(\dfrac{33}{2}\).....\(\dfrac{60}{2}\)

=\(\dfrac{31.32.33.....60}{2^{30}}\)

=\(\dfrac{\left(1.2.3.....30\right).\left(31.32.33.....60\right)}{\left(1.2.3.....30\right).2^{30}}\)

=\(\dfrac{1.2.3.....60}{2.4.6.....60}\)

=\(\dfrac{\left(1.3.5.....59\right).\left(2.4.6.....60\right)}{2.4.6.....60}\)

=1.3.5.....59

Vậy (đpcm)